Question

Find the zeroes of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients.
a)3x^2-5x+2=0
b)6x^2-x-2=0
c)x^2-3x-10=0​

Answer 1

Answer:

3x^2-5x+2=0

on factorising by middle term splitting we get

3x^2-3x-2x+2=0

3x(x-1)-2(x-1)=0

(3x-2)(x-1)=0

there are two real roots or zeroes

3x-2=0 and x-1=0

x=2/3 or 1

verification,

putting x =2/3 in the given quadratic equation

we get

3×1^2-5×1+2

=0 hence verified

putting X=2/3

3×(2/3)^2-5×2/3+2

=3×4/9-10/3+2

=4/3+2-10/3

10/3-10/3

=0

all of them can be solved similarly